By [1]}, when the empirical estimates for
\(\mathbb {E}(Y|{\mathbf {X}})\)  and \(\mathbb {E}(Y|{\mathbf {X}}_{-j})\)  converge to the target functions \(f_0\)  and \(f_{0,-j}\)  at the rate of \(O_p(n^{-1/4})\)  in function norm, we achieve an asymptotically normal and efficient estimator for the VI measure. In this section, we give a theoretical guarantee to show that the lazy prediction \(h_{\theta _f + \Delta \theta _j}(X^{(j)})\)  for the reduced model achieves such convergence rate, so that the lazy training procedure gives an accurate estimate of VI with an error in the order of \(O(\frac{1}{\sqrt{n}})\)  and we can make inference accordingly.
